Question

How do you simplify and divide `(z^5-3z^2-20)div(z-2)`?

Answer 1

`z^4+2z^3+4z^2+5z+10`

Explanation:

Since, `z=2` satisfies the polynomial `z^5-3z^2-20` hence `z-2` is a factor `z^5-3z^2-20` i.e. `z^5-3z^2-20` is completely divisible by `z-2`. It can be factorized as follows

`z^5-3z^2-20`#

`=z^4(z-2)+2z^3(z-2)+4z^2(z-2)+5z(z-2)+10(z-2)`

`=(z-2)(z^4+2z^3+4z^2+5z+10)`

`\frac{z^5-3z^2-20}{z-2}=z^4+2z^3+4z^2+5z+10`